Although I took anatomy, I still was under the illusion that there are only two genders male and female. So what is gender identity? One get to pick and choose who they are?

Been there done that. I was always Mickey Mantle as I was growing up and playing baseball. Then I grew up.

It's amusing how often one will see some version of the above, either IRL or online or some other media. The speaker usually thinks this is really something profound and salt-of-the-earth stuff (as Dunning-Kruger would predict).

As for you "[taking] anatomy" - are you seriously saying you've never run across the reality of intersex children and sex assignment?

And beyond the anatomical reality of intersex individuals, you've never heard of the notion that gender is between the ears, and sex is between the legs?